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Math Help - Tricky Transposition of Formula

  1. #1
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    Smile Tricky Transposition of Formula

    Hi there, I am studying for an engineering degree, and need to transpose this formula. I'm normally ok at this, however on this particular one I keep getting a very slightly different answer to the text book.

    I need to transpose this for (A2):

    q=(A)squareroot[(2gh/(A/A2)^2 -1]

    Sorry about the messy presentation, I don't know how to use the code to make nice formulas! The bit in [square brackets] is all uner the squareroot.

    Just ask if your not sure how the original formula reads.

    I got an answer of:

    A2=+/- squareroot[(q^2)(A^2)-q^2/2ghA2]

    In the text book, the -q^2 is +q^2 and is on the bottom of the fraction.

    Any help with this would be greatly appriciated.

    Thanks in advance, Mike
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  2. #2
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    Quote Originally Posted by mikewhant View Post
    I need to transpose this for (A2):

    q=(A)squareroot[(2gh/(A/A2)^2 -1]
    please clarify ...

    q = A\sqrt{\frac{2gh}{\left(\frac{A}{A_2}\right)^2 - 1}}

    or

    q = A\sqrt{\frac{2gh}{\left(\frac{A}{A_2}\right)^2} - 1}


    what you posted is the second interpretation.
    Last edited by skeeter; January 4th 2010 at 02:43 PM. Reason: insert omitted exponents
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  3. #3
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    Smile

    Hello,

    It is the first one you posted. Sorry about that!

    Thanks, Mike
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  4. #4
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    q = A\sqrt{\frac{2gh}{\left(\frac{A}{A_2}\right)^2 - 1}}

    \frac{q}{A} = \sqrt{\frac{2gh}{\left(\frac{A}{A_2}\right)^2 - 1}}

    \frac{q^2}{A^2} = \frac{2gh}{\frac{A^2}{A_2^2} - 1}

    \frac{q^2}{A^2} = \frac{2A_2^2gh}{A^2 - A_2^2}

    q^2(A^2 - A_2^2) = 2A^2A_2^2gh

    q^2A^2 = 2A^2A_2^2gh + q^2A_2^2

    q^2A^2 = A_2^2(2A^2gh + q^2)

    \frac{q^2A^2}{2A^2gh + q^2} = A_2^2

    \pm \sqrt{\frac{q^2A^2}{2A^2gh + q^2}} = A_2

    what a mess ...
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  5. #5
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    Smile

    Thanks alot, I was going wrong on the 4th line.

    Take care and thanks again!

    Mike
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